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Titlebook: Buildings of Spherical Type and Finite BN-Pairs; Jacques Tits Book 1974 Springer-Verlag Berlin Heidelberg 1974 Finite.Morphism.algebra.alg

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Buildings of type F4,A total ordering (resp. a numbering from 1 to 4) of the vertices of the diagram F. is called . if two consecutive vertices are joined by a single or double stroke (resp. if the ordering determined by this numbering is natural).
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Appendix 1. Shadows,In 6.3, 7.4, 7.12, 10.13, we have seen that the study of weak buildings of the types A., C., D., F. is equivalent to the study of some “spaces” (projective spaces, polar spaces, etc.). The methods we have used to associate spaces to buildings are special cases of a general procedure which we shall describe here.
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Coxeter complexes,t C′, which means, in other words, that there exists a folding of Σ which maps C′ onto C. . Σ .. The group generated by all reflections of a Coxeter complex Σ will be denoted by W(Σ) and called the . of Σ.
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Teubner Studienbücher Mathematikonditions hold:. It is clear that Δ is a chamber complex and that the apartments are isomorphic subcomplexes. We shall see (3.15) that the isomorphism class of the apartments is entirely determined by Δ. More precisely, it can be shown that if a complex Δ possesses a set α of subcomplexes such that
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Teubner Studienbücher Mathematikned over some field k, the group of k -rational points of X over k is denoted by X(k) (instead of X., as in [8]; the notations Z( ), R( ), R.( ) stand for “centralizer of”, “radical of”, “unipotent radical of” respectively; the group of all automorphisms (resp. all special automorphisms) of a buildi
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